{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2VNHSQGO7DD52C5QSTRLQVHP4U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b9888eb68dd11a2a34a747cda6d9de2dc933203ee4a7ce5620a731897d2d3c3e","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.HO","submitted_at":"2005-04-14T03:07:11Z","title_canon_sha256":"5da182cbcc5a682f3cbb14c0c3853cde515acbcfdd751460cb88787b773d3fc3"},"schema_version":"1.0","source":{"id":"math/0504289","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504289","created_at":"2026-07-04T14:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504289v3","created_at":"2026-07-04T14:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504289","created_at":"2026-07-04T14:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"2VNHSQGO7DD5","created_at":"2026-07-04T14:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"2VNHSQGO7DD52C5Q","created_at":"2026-07-04T14:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"2VNHSQGO","created_at":"2026-07-04T14:39:53Z"}],"graph_snapshots":[{"event_id":"sha256:97c5bd3c74e897cafe58a9128922466b89ef1caa406cc76ec2a1f96030947bc7","target":"graph","created_at":"2026-07-04T14:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0504289/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit numerical error estimates and computations of the Mertens \"constant,\" both of which are missing from modern expositions. In as much as his strategy and techniques are quite different from today's methods, his original methods deserve to be better known.","authors_text":"Mark B. Villarino","cross_cats":["math.NT"],"headline":"","license":"","primary_cat":"math.HO","submitted_at":"2005-04-14T03:07:11Z","title":"Mertens' Proof of Mertens' Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504289","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0602ca291fe5b346899e492c28274f4bc2d35b8fd6b55f2204923e0f71443935","target":"record","created_at":"2026-07-04T14:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b9888eb68dd11a2a34a747cda6d9de2dc933203ee4a7ce5620a731897d2d3c3e","cross_cats_sorted":["math.NT"],"license":"","primary_cat":"math.HO","submitted_at":"2005-04-14T03:07:11Z","title_canon_sha256":"5da182cbcc5a682f3cbb14c0c3853cde515acbcfdd751460cb88787b773d3fc3"},"schema_version":"1.0","source":{"id":"math/0504289","kind":"arxiv","version":3}},"canonical_sha256":"d55a7940cef8c7dd0bb094e2b854efe503f9436d47e67979aaf4e86e63e3924f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d55a7940cef8c7dd0bb094e2b854efe503f9436d47e67979aaf4e86e63e3924f","first_computed_at":"2026-07-04T14:39:53.899674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:53.899674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VTanpJV3hRGpI0AO80GAYneZpsssHuNh9E+RxaiQbn+aDLhmSc0fc3UfvArRuS3eDl+Y79RaLSpOQqLz9E/kAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:53.900102Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504289","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0602ca291fe5b346899e492c28274f4bc2d35b8fd6b55f2204923e0f71443935","sha256:97c5bd3c74e897cafe58a9128922466b89ef1caa406cc76ec2a1f96030947bc7"],"state_sha256":"a1b92a14f19c3e2bd8b802e63f2ad61371e6ec959cd4a1f15f66071639fa3d91"}